Vi deler en halv kake.

Because Norwegian usually follows subject + verb + object word order in a normal main clause.

• Vi = subject
• deler = verb
• en halv kake = object

So Vi deler en halv kake is the standard pattern, just like We share half a cake in English.

Norwegian word order can change in some cases, but then the verb still normally stays in second position:

• I dag deler vi en halv kake. = Today we are sharing half a cake.

Deler is the present tense of å dele.

It can mean:

• to divide
• to split
• to share

In this sentence, it most naturally means share or split.

Examples:

• Vi deler pizzaen. = We share the pizza.
• Hun deler eplet i to. = She splits the apple in two.

So å dele is a very useful verb for both physical dividing and sharing something with someone.

En halv kake means half a cake.

Here:

• en = a
• halv = half
• kake = cake

Norwegian commonly uses this structure:

• en halv kake = half a cake
• et halvt eple = half an apple

So halv works like a quantity word here, describing how much of the noun there is.

Because kake is a common-gender noun in Norwegian, and in this kind of expression Norwegian normally uses the indefinite article.

So:

• en kake = a cake
• en halv kake = half a cake

This is very similar to English, where we say half a cake.

You will often see:

• en halv time = half an hour
• en halv liter = half a liter

Because halv changes form to match grammar.

Common forms are:

• halv with en-words
  
  • en halv kake
• halvt with et-words
  
  • et halvt eple
• halve in plural or some definite forms
  
  • to halve brød
  • den halve kaken

So in en halv kake, kake is an en-word, which is why the form is halv.

Not usually.

The sentence most naturally means we are sharing half a cake or we are splitting half a cake.

It does not normally mean that each person gets half a cake. If you wanted to be clearer about that, you would say something like:

• Vi får et halvt kakestykke hver.
• Vi får en halv kake hver.

So the original sentence describes one half-cake portion being shared.

Yes. That is one of the small ambiguities of å dele.

Depending on context, it can mean:

• share
• divide up
• split

So Vi deler en halv kake could mean:

• We share half a cake.
• We split half a cake into parts.

In everyday use, those ideas are often very close, so context decides the exact nuance.

This is an important difference:

• en halv kake = half a cake
  This is indefinite.
• den halve kaken = the half cake / the half of the cake
  This is definite.

Examples:

• Vi deler en halv kake. = We share half a cake.
• Vi spiser den halve kaken. = We eat the half cake / the half of the cake.

In Norwegian, definite noun phrases often use both:

• a definite marker before the adjective: den
• a definite noun ending: kaken

Kake is an en-word in Bokmål.

So:

• en kake = a cake
• kaken = the cake

Because it is an en-word, the phrase becomes:

• en halv kake

If it were an et-word, you would expect et halvt ... instead.

A simple pronunciation guide is:

Vi deler en halv kake
vee DEH-ler en halv KAH-keh

A few notes:

• vi sounds like vee
• deler has two syllables: de-ler
• halv often has a clear v sound at the end, though connected speech can soften things a bit
• kake has two syllables: ka-ke

The pitch accent and exact vowels depend on dialect, but the standard Bokmål-style pronunciation above is a good starting point.

Normally, no. In standard Norwegian, you would usually say en halv kake.

Without en, it sounds incomplete or unnatural in this sentence.

So the natural form is:

• Vi deler en halv kake.

Just as in English you would normally say half a cake, Norwegian also keeps the article here.